Lin-Yu Miao

Classical Solutions for a Finite-Horizon Exit-Time Problem with Degenerate Diffusion Control

We study finite-horizon exit-time control of a one-dimensional affine diffusion, with an unbounded control acting on both drift and volatility. Since an admissible control can cancel the instantaneous volatility, the associated HJB equation is not uniformly parabolic. Moreover, the location of the degeneracy is not pre...